A man’s age is three times his son’s age. Ten years ago he was fivetimes his son’s age. By forming two equations and solving themsimultaneously, find both of their ages.
Question
A man’s age is three times his son’s age. Ten years ago he was fivetimes his son’s age. By forming two equations and solving themsimultaneously, find both of their ages.
Solution
Let's denote the man's current age as M and his son's current age as S.
From the problem, we have two equations:
-
M = 3S (The man’s age is three times his son’s age)
-
M - 10 = 5(S - 10) (Ten years ago the man was five times as old as his son)
Now we can solve these equations simultaneously.
First, substitute M from the first equation into the second equation:
3S - 10 = 5S - 50
Rearrange the equation:
50 - 10 = 5S - 3S
40 = 2S
So, S = 20
Substitute S = 20 into the first equation:
M = 3 * 20 = 60
So, the man is 60 years old and his son is 20 years old.
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